Change start frame of a background movie clip?
Movie Clip is a special data type in Blender. To change its properties you would have to go the Movie Clip Editor, open up the clip there, open the properties panel (N), go to footage settings and add an offset there in order to change the start frame. 

However, if you only want to have a background video, I would advise you not to use the Movie Clip type. Instead, click on 'Image', and open up your video. There you can also adjust the offset in order to change the video's startframe.